For most people you move an event forward by scheduling it to happen sooner, but other people imagine the event being moved forward into the future, postponed. This is what most—but not all—people mean by saying they want to move an event back—later. Usage is also split on whether moving an event up means making it happen sooner (most common) or later (less common). The result is widespread confusion. When using these expressions make clear your meaning by the context in which you use them. “We need to move the meeting forward” is ambiguous; “we need to move the meeting forward to an earlier date” is not.
Just to confuse things further, when you move the clock ahead in the spring for daylight saving time, you make it later; but when you move a meeting ahead, you make it sooner. Isn’t English wonderful?